UWB_Lecture02_v2 - Ultrawideband systems: Fundamentals and...

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1 1 Ultrawideband systems: Fundamentals and Standardization Lecture 2 Min-Kuan Chang National Chung Hsing University 教育部通訊教改計畫 教育部通訊教改計畫 2 Outline • How To Define Bandwidth • Time-modulated UWB (Impulse radio) • Direct Sequence (DS) UWB
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2 3 How To Define Bandwidth 4 How To Define Bandwidth • Given the power spectral density of a signal f How to specify the bandwidth of a signal ( ) Sf () st
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3 5 How To Define Bandwidth • To simplify the lines of definition, we make the following assumptions – Symmetric around zero – Monotonic decreasing after zero – The total power is equal to 1 – The maximum of occurs at ( ) ( ) f S f S = () ( ) 21 1 2 for 0 Sf f f ≤≤ - 1 Sf d f = ( ) 0 f = ( ) ( ) max 0 f Sf S = 6 How To Define Bandwidth • Four common ways to define the bandwidth – The rms bandwidth (Gabor bandwidth) • The standard deviation of PSD, – The 3dB bandwidth • This bandwidth is described as any solution of the equation • It indicates a value of f at which is half its peak value 1 2 2 - rms Bf S f d f = rms B ( ) 3 1 (0) 2 db SB S = 3 db B ( )
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4 7 How To Define Bandwidth • Four common ways to define the bandwidth – The equivalent rectangular bandwidth • The definition simply matches the area under to the area of a rectangle with height and width 1 (0) 2 ( ) 1 - 2( 0 ) er er S B S f df B S ⋅= = ⇒= er B er B er B ( ) Sf ( ) max f 8 How To Define Bandwidth • Four common ways to define the bandwidth – The x fractional power bandwidth • It is described implicitly as any solution to - () xF xF B B S f df x = xF B
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5 9 How To Define Bandwidth •P rob l em – How to substitute one measure for another – Let be the collection of all functions satisfying • Symmetric around zero • Monotonic decreasing after zero • The total power is equal to 1 • The maximum of occurs at Ω ( ) ( ) f S f S = ( ) ( ) 21 1 2 for 0 Sf f f ≤≤ - () 1 Sf d f = ( ) 0 f = ( ) ( ) max 0 f Sf S = 10 How To Define Bandwidth • To deal with this problem, we define – Given measure is known, we can have the idea of the range of A s B BS Max ∈Ω ⎩⎭ Two different measures B B A B A A B s B BM a x B ⎧⎫ ⎪⎪ × ⎨⎨
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6 11 How To Define Bandwidth 1 1 1 1 () A B Bs rms B er B 3 dB B xF B rms B er B 3 dB B xF B s Max B A 3 3 2 31 x 2 1 x 2 x x 12 How To Define Bandwidth • Suppose we wish to communicate using a set of M waveforms , – Defined in the interval – The probability of choosing , is equal to ( ) n st 1, 2, , nM = " ( ) 0, T ( ) n s t , = " 1 M {} 2 1 1 M n n Sf Fst M = =
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7 13 How To Define Bandwidth • The dimensionality of the signal set is the smallest number N of orthonormal functions such that • If we define a signal coefficient matrix ,then the performance is solely dependent on this matrix ( ) , n=1,2, ,N n gt " () () 1 N mm n n n st sgt = = [] mn s Λ = ( ) n G f 14 How To Define Bandwidth • To make use of the bandwidth efficiently, what set of basis functions yields an energy spectral density of minimum bandwidth given the signal coefficient matrix?
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This note was uploaded on 09/27/2010 for the course UWB 164 taught by Professor Minkuan during the Fall '01 term at National Cheng Kung University.

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UWB_Lecture02_v2 - Ultrawideband systems: Fundamentals and...

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